总分化——地球科学堆栈交换江南电子竞技平台江南体育网页版 最近30从www.hoelymoley.com 2023 - 07 - 07 - t20:18:55z //www.hoelymoley.com/feeds/question/19801 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/19801 3 总分化 duff18 //www.hoelymoley.com/users/20566 2020 - 06 - 05 - t09:41:19z 2020 - 07 - 10 - t15:50:04z < p >本地导数与全导数:< / p > < p > <跨类= " math-container " > \美元压裂{\部分T}{\部分T} = \压裂{DT} {DT} - \ mathbf{你}\ cdot \微分算符台币< / span > < / p > < p > - < span class = " math-container " > $ \ mathbf{你}\ cdot \微分算符台币< / span >项代表了由平流变化。< / p > < p >所以,例如冷空气吹在温暖的地区气温将冷平流,它会对当地造成负面影响的导数。< / p > < p >我很难解读<跨类= " math-container " > $ \压裂{DT} {DT} $ < / span >。如果它代表温度变化在流无论流冷却器/温暖的地区移动,这是由于什么?说的扩张和顺向冷却空气包裹吗? < / p > //www.hoelymoley.com/questions/19801/-/19802 # 19802 2 BarocliniCplusplus回答的完全分化 BarocliniCplusplus //www.hoelymoley.com/users/704 2020 - 06 - 05 - t15:04:10z 2020 - 06 - 05 - t15:04:10z < p >的问题”这可以导致什么?”,有各种各样的原因。让我们看看< a href = " http://glossary.ametsoc.org/wiki/First_law_of_thermodynamics " rel = " nofollow noreferrer " >热力学第一定律< / >(包括分子扩散):< span class = " math-container " > $ $ \压裂{DU} {Dt} = c_p \压裂{Dt} {Dt} = qp \压裂{D \α}{Dt} + \ν\微分算符^ 2 U $ $ < / span >, < span class = " math-container " >在U < / span >是美元< a href = " http://glossary.ametsoc.org/wiki/Internal_energy " rel = " nofollow noreferrer " >理想气体的内能< / >,< span class = " math-container " > Q < / span >是美元非绝热加热,< span class = " math-container " > p < / span >是压力,美元和<跨类= " math-container " > \α< / span >是美元的特定体积,< span class = " math-container " > \ν< / span >美元是分子扩散系数,和<跨类= " math-container " > c_p < / span >美元是等压比热容。< / p > < p >,没有非绝热加热,一种方法是改变音量或压力,随海拔的变化最变化(你可以重写< span class = " math-container " > $ p \压裂{D \α}{Dt} $ < / span > < span class = " math-container " >任期美元\α\压裂{Dp} {Dt} \大约\α\压裂{\部分p}{部分z \} \大约\α\ρg = g = - \ Gamma_d c_p $ < / span >, < a href = " http://glossary.ametsoc.org/wiki/Dry-adiabatic_lapse_rate " rel = " nofollow noreferrer " > <跨类= " math-container " > \ Gamma_d < / span >是美元干绝热递减率< / >)。使用这种关系,(1)可以写成< span class = " math-container " > $ $ \压裂{\部分T}{\部分T} = \压裂{Q} {c_p} + \ν\微分算符^ 2 T - \压裂{g} {c_p} - \ Gamma_d vec{你}\ \ cdot \ T微分算符$ $ < / span >的另一种方法是通过分子热量交换,它是如此的小通常是被忽视的,除非是在一个micrometeorological上下文。还有非绝热加热,也许最加载项的方程。< / p > < p >传热熵加热是任何加热源,需要改变。这包括潜热交换,辐射加热,等。湍流混合可能可以说是在这个大尺度,但不是小尺度。< / p > //www.hoelymoley.com/questions/19801/-/19924 # 19924 0 她回答的完全分化 //www.hoelymoley.com/users/8396 2020 - 07 - 10 - t15:50:04z 2020 - 07 - 10 - t15:50:04z < p >我将重写你的方程在一个更自然的秩序,至少对我来说:< / p > < p > <跨类= " math-container " > $ $ \压裂{DT} {DT} = \压裂{\部分T}{\部分T} + \ mathbf{你}\ cdot \ T微分算符$ $ < / span > < / p > < p > <跨类= " math-container " >一词\压裂{DT} {DT}美元的全导数是< / span > < span class = " math-container " > T < / span >美元对时间,即温度如何变化(在地球上一个特定的地方),随着时间过去,可以有不同的原因。< span类=”一词math-container " > \美元mathbf{你}\ cdot \微分算符< / span >新台币,正如你指出的那样,是平流项。它表达了,风可以带来温暖或凉爽空气到这个地方,让它过冷或过热,如冷空气。< / p >

The term $\frac{\partial T}{\partial t} $ expresses the $local$ change of temperature with time. If no winds are blowing, temperature may change as well, for example due to insolation (cooler at night, warmer during the day), seasonality and so on.

Therefore, the term $\frac{DT}{Dt}$ on the left-hand side of the equation makes it maybe it more clear. It is not a component of the derivate, it is the total derivative, decomposed in local and advective terms. So advection is one of the components of $\frac{DT}{Dt}$.

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